Leavitt Path Algebras

This thesis consists of five chapters. In the first chapter, basic knowledge and history of Leavitt path algebras and the aim of the thesis are given. In the second chapter, some fundamental definitions and theorems of ring and module theory, and graph theory are mentioned. The third chapter deals with the properties of Leavitt path algebras with coefficients over an arbitrary field $K$, denoted $L_K(E)$. It is proved that the Jacobson radical of Leavitt path algebras is zero, $J(L_K(E))=0$, and that $L_K(E)$ is a semiprime ring. In the next chapter, Leavitt path algebras with coefficients over unital commutative ring $R$, denoted $L_R(E)$, are studied. It is shown that if $R$ is an integral domain, then $L_R(E)$ is a semiprime ring. Moreover, a unital commutative ring $R$ is a semiprime ring if and only if $L_R(E)$ is a semiprime ring. In the last chapter, the results of the research and some suggestions for researchers are given.